Ultrafast Pulse Shaping and Applications

Ultrafast Pulse Shaping and Applications Andrew M. Weiner Purdue University http://ece.www.ecn.purdue.edu/~amw CLEO, May 2010

Fourier Transform Pulse Shaping: Outline Pulse shaping basics Results from pulse shaping theory Programmable pulse shaping: spatial light modulators Selected applications Polarization pulse shaping Pulse shaping at high spectral resolution Not covered Most other types of pulse shaping (e.g., direct space-to-time shapers) Measurement techniques etc.

Pulse Shaping by Linear Filtering ( ) ( ) e out (t) = dt h t t ein t E ( ω ) = H( ω)e ( ω) out in

Spectral Dispersers: Gratings Prisms VIPAs AWGs Femtosecond Pulse Shaping 4f configuration inherently dispersion-free Fourier synthesis via parallel spatial/spectral modulation Diverse applications: fiber communications, coherent quantum control, few cycle optical pulse compression, nonlinear microscopy, RF photonics Pulses widths from ps to few fs; time apertures up to ~1 ns Review article: A.M. Weiner, Rev. Sci. Instr. 71, 1929 (2000)

Pulse Shaping Data (Intensity Cross-correlation) E(ω) ω ω Temporal analog to Young s two slit interference experiment Highly structured femtosecond waveform obtained via simple amplitude and phase filtering Weiner, Heritage, and Kirschner, J. Opt. Soc. Am B 5, 1563 (1988).

Synthesis of Femtosecond Square Pulses Shaping via microlithographic amplitude and phase masks Amplitude mask: gray-level control via diffraction out of zero-order beam Cross-correlation data Power spectrum Theoretical intensity profile Weiner, Heritage, and Kirschner,J. Opt. Soc. Am B 5, 1563 (1988).

Pulse Shaping via Spectral Phase Control Shaping via liquid crystal modulator array (LCM) Linear phase Quadratic phase Cubic phase ψ ω = B ψ ω = C ω ω ( ) A( ω ω ) o ( ) τ ω = ψ ( ω) ω ψ( ω ) = ( ω ω ) 2 ( ) ( ) 3 o o A>0 A=0 A<0 chirp compensated chirped Pulse position modulation Linear chirp Weiner et al, IEEE J. Quant. Electron. 28, 908 (1992) Nonlinear chirp Efimov et al, J. Opt. Soc. Am. B12, 1968 (1995)

Shaping of Incoherent and Nonclassical Light Incoherent Light: Shaping the elec. field cross-correlation function ASE source (EDFA) Pulse shaper No shaping PD Spectrum & spectral phase Nonclassical Light: Shaping the two-photon wave function Entangled photon source (parametric down-conversion) Signal Idler Pulse shaper Ultrafast coincidence detector (sum frequency generation) Signal Idler Linear spectral phase 1020 1060 1100 Wavelength (nm) Sum frequency counts 1020 1060 1100 Wavelength (nm) -4 0 4 Delay (ps) Wang and Weiner, Opt. Comm. 167, 211 (1999) Signal-idler delay (fs) Pe er, Dayan, Friesem, and Silberberg, Phys. Rev. Lett. 94, 073601 (2005) -500 0 500-500 0 500 Signal-idler delay (fs)

Results from Pulse Shaping Theory

The Complexity of a Shaped Pulse spectral resolution ~ 1/time aperture (T) bandwidth time aperture pulse duration ~ 1/bandwidth (B) Time-bandwidth product (BT = B/δf = T/δT) provides a measure of potential complexity of a shaped pulse Equal to # of independent features in either frequency or time domain Favors large optical bandwidth / very short pulses Spectral resolution (and time aperture) limited by minimum SLM feature size, finite optical spot size

Pulse Shaping Theory (I): Basics ( ω ) = ( αω ) ( ω ) E M E out in x α = = ω spatial dispersion e (t) e (t) m(t / ) out = α ( ) j ω t in 1 m(t / α ) = M αω e dω 2π For a transform-limited input pulse, pulse shaping generally does not decrease the pulse duration (bandwidth is not increased).

Pulse Shaping Theory: Effect of Diffraction Assume spatial filter selects fundamental Gaussian mode (e.g., single-mode fiber, regenerative amplifier) ( ) ( ) 2 2 E ω ~ dx M(x) exp -2 x-αω w E ( ω) out o in ( ) Filter function e 2 2 2 out (t) ~ e in (t) m(t / α) exp wot / 8α Spectral smearing due to finite spot size time window Equivalent to a window function in the time domain Thurston, Heritage, Weiner, and Tomlinson, IEEE JQE 22, 682 (1986); A.M. Weiner, Ultrafast Optics (Wiley, 2009)

Phase-to-Amplitude Conversion due to Diffraction Pseudorandom phase mask with abrupt 0-π phase transitions Each phase transition leads to a deep hole in the power spectrum. Such data validate theoretical treatment of diffraction effects in pulse shaping. Sardesai, Chang, and Weiner, J. Lightwave Tech. 16, 1953 (1998)

Programmable Pulse Shapers: Spatial Light Modulators

Fourier Transform Pulse Shaping A variety of programmable modulator arrays Nuernberger, Vogt, Brixner and Gerber, Phys. Chem. Chem. Phys. 9, 2470 (2007)

Programmable Pulse Shaping Liquid Crystal Modulator (LCM) Arrays Weiner et al, IEEE JQE 28, 908 (1992) Wefers and Nelson, Opt. Lett. 20, 1047 (1995) One layer LCM: phase-only shaping Two layer LCM: independent amplitude and phase shaping ~400-1600 nm typical wavelength range - recently extended to 260 nm in the UV [(Tanigawa et al, Opt. Lett. 34, 1696 (2009)] Tens of milliseconds response time

1-layer LCM schematic Liquid Crystal Modulator Array (LCM) No applied voltage With applied voltage Longitudinal field tilts molecules, changing birefringence Typically 128-640 pixels on 100 µm centers Phase vs. voltage response 1-layer LCMs: input polarization (ŷ) aligned with LC molecules (ŷ) for phase-only response 2-layer LCMs: input polarization (ŷ) vs. ±45 for LC molecules for phase-amplitude response Phase change 2π 0 10 Voltage (rms)

Conventional LC Geometry Two liquid crystal layers, aligned at ±45 -Phase and amplitude control or -Phase and partial polarization control Two LC layers successively rotate polarization about 45 o point Birefringence axis Polarization rotation depends on arc length (retardance) difference with polarizer: gray-level amplitude control Phase modulation depends on total arc length (total retardance) Poincare sphere Polarization control limited to a subset of polarization space

Pulse Shaping Results Using Phase and Amplitude (2-Layer) LCM Square pulse Pulse sequence Pulse sequence with different chirp rates -2 0 2 Time (ps) -2-1 0 1 2 Time (ps) -2-1 0 1 2 Time (ps) Independent phase and amplitude control allows generation of nearly arbitrarily shaped waveforms. Kawashima, Wefers, and Nelson, Annu. Rev. Phys. Chem. 46, 627 (1995)

Liquid Crystal on Silicon (LCOS) Technology Thousands to millions of tiny pixels with phase-only response single frequency (ω) Conventional LCM ω + δω 100 µm [1D] LCOS array single frequency http://rvlab.icg.tugraz.at/ 1.6 µm

Pulse Shaping via Liquid Crystal on Silicon (LCOS) SLMs Amplitude and phase shaping with phase-only reflection modulators... single frequency... One-dimensional SLM device, 1 X 12,288 pixels, zero-order geometry Applied phase 1.6 µm average phase Φ(x) 2πx M(x) = exp i (x)sin i (x) g + Φ Λ Diffraction losses controlled by phase excursion (2 ) Position or pixel number Over-sampling permits phase and amplitude control by diffracting power out of zero-order beam Wilson, Schlup, and Bartels, Optics Express. 15, 8979 (2007)

Two-dimensional SLM device, 1920 X 1080 pixels 8 µm 2D LCOS Arrays single frequency Several novel applications Generate 1D array of shaped waveforms Rapid waveform update by scanning a 1D waveform array Radically increased waveform complexity via 2D pulse shapers Zero order geometry (lowest insertion loss) First order diffraction geometry (best extinction ratio) Frumker and Silberberg, J. Opt. Soc. Am. B 24, 2940 (2007)

RF arbitrary waveform generator Programmable Pulse Shaping Acousto-optic modulators (AOM) Vibrates and changes refraction index Spectral amplitude-phase shaping via diffraction from a traveling acoustic wave Traveling-wave mask; generally applicable only to amplifier systems; reprogramming time ~ 10 µs (device dependent) Electronic arbitrary waveform generator provides amplitude-phase control, but care needed to account for acoustic attenuation and nonlinearities Dugan, Tull, and Warren, J. Opt. Soc. Am. B 14, 2348 (1997)

Programmable Pulse Shaping Acousto-optic modulators (AOM) ~800-nm pulse sequence exhibiting constant, linear, quadratic, cubic, and quartic spectral phases Mid-IR pulse shaping using Ge AOM RF drive Spectrum Dugan, Tull, and Warren, J. Opt. Soc. Am. B 14, 2348 (1997) 260 nm 5 µm demonstrated wavelength range Shim, Strasfeld, Fulmer, and Zanni, Opt. Lett. 31, 838 (2006) Continuous spatial modulation (time-bandwidth products of several hundred)

Acousto-optic Programmable Dispersive Filter (AOPDF) An in-line pulse shaping technology especially for amplified systems Phase matched polarization conversion mediated by acoustic wave Due to birefringence, output temporal profile related to acoustic spatial profile (controlled by radio-frequency arbitrary waveform generator) Representative numbers: 2.5 cm TeO 2 crystal, n 2 -n 1 =0.04 Acoustic velocity: 10 5 cm/s Acoustic frequencies: 20 MHz around 52.5 MHz Optical frequencies: 150 THz around 375 THz (800 nm) Time aperture for pulse shaping: 3.3 ps Acoustic transit time: 25 µs Verluise, Laude, Cheng, Spielmann, and Tournois, Opt. Lett. 25, 575 (2000) ULTRAFAST OPTICS AND OPTICAL FIBER COMMUNICATIONS LABORATORY

Acousto-optic Programmable Dispersive Filter (AOPDF) Typical system configuration Reduced rep rate applications (e.g., amplified systems) preferred due to traveling-wave character of acoustic mask Acoustic update rate governed by acoustic transit time fast enough for fsec amplifiers Time apertures of picoseconds; time-bandwidth products of hundreds Crystal dispersion must be compensated, either by AOPDF itself or by external means Wavelength coverage from 250 nm 2700 nm ULTRAFAST OPTICS AND OPTICAL FIBER COMMUNICATIONS LABORATORY

Selected Applications

Control Strategies for Femtosecond Pulse Shaping Open loop control Requires pulse shaper calibration and specification of input and output pulses Adaptive control Requires specification of an observable to be optimized Sample application: coherent quantum control, where the Hamiltonian may not be known with sufficient precision

Multiple-Pulse Control of Impulsive Stimulated Raman Scattering Periodic pulse sequences realized via periodic spectral phase shaping (α-perylene) Single pulse excitation Time response X10 Frequency response Time (ps) Frequency (THz) Pulse sequence excitation Pulse sequence Time response Fsec pulse sequences allow selective amplification of optical phonons matched to the pulse repetition rate. Weiner, Leaird, Wiederrecht, and Nelson, Science 247, 1327 (1990); J. Opt. Soc. Am. B8, 1264 (1991) Time (ps) Time (ps)

Quantum Control of Two Photon Absorption in Cesium 2 Sinusoidal spectral phase ψ( ω ) = α cos ω ωo ψ( ω ) = α sin ω 2 Anti-symmetric around ω ο /2 ω 2 o E 1 Narrowband TPA 1 Dark Pulse no TPA! Symmetric around ω o /2 Shaping spectral phase to manipulate interference between two photon absorption pathways for creation of user selectable dark or light pulses Similar effects occur in second harmonic generation later applied for MIIPS pulse measurement technique Meshulach and Silberberg, Nature 396, 239 (1998)

Chemically Selective Nonlinear Microscopy Periodic spectral phase plus short wavelength block Shaped pulse: max CARS Single-pulse CARS images: CH 2 Br 2 in glass capillary plate Dudovich et al, Nature 418, 512 (2002) 45µm Shaped pulse: min CARS Difference Transformlimited Silberberg, Annu. Rev. Phys. Chem. 60, 277 (2009) Pulse shape selected to emphasize spectral feature of interest Simple in-line geometry, with programmable dispersion control Pulse shaping also reduces nonresonant background

Pulse Shaping Applications in Ultrafast Optical Science Adaptive Control Quantum control of photofragmentation Enhancement of high harmonic generation Quantum control of energy flow in light harvesting Assion et al, Science 282, 919 (1998) Changing the pulse shape changes the ratio of photofragmentation products Bartels et al, Nature 406, 164 (2000) Programming the pulse shape for constructive interference of x-ray bursts from successive light cycles for selective enhancement of individual harmonics Herek et al, Nature 417, 533 (2002) Shaping the phase of the light field mediates energy transfer branching ratios in complex light harvesting biomolecules

Applications in Optical Communications Dynamic spectral processor Spectral disperser Spectral combiner Broadband input - Ultrashort pulse - CW plus modulation Processed output - Multiple wavelengths Spatial light modulator Control of phase, intensity, polarization Frequency-by-frequency, independently, in parallel -Pulse shaping -Dynamic spectral equalizers -Dynamic wavelength processing

Pulse Shaping in WDM: Intensity Control Manipulation on a wavelength-by-wavelength basis No concern for phase or for coherence between channels Wavelength selective add-drop multiplexer (and wavelength selective switches) Ford et al, J. Lightwave Tech. 17, 904 (1999) [Lucent] Spectral gain equalizer MEMS version Liquid crystal version: Patel and Silberberg, IEEE PTL 7, 514 (1995) Ford et al, IEEE JSTQE 10, 579 (2004) [Lucent]

Programmable Fiber Dispersion Compensation Using a Pulse Shaper: Subpicosecond Pulses Spectral phase equalizer Coarse dispersion compensation using matched lengths of SMF and DCF Fine-tuning and higher-order dispersion compensation using a pulse shaper as a programmable spectral phase equalizer Similar ideas apply to DWDM tunable dispersion compensation and few femtosecond pulse compression. A.M. Weiner, U.S. patent 6,879,426 ( ) τ ω = ψ ( ω) ω

Intensity cross-correlation (a.u.) 460 fs transmission over 50 km SMF Commercial DCF module (as is) with spectral phase equalizer without DC by pulse shaper second-order DC by pulse shaper both second- and thirdorder DC by pulse shaper Essentially distortion-free! -10-5 0 5 10 15 20 Time (ps) Phase (rad) 100 80 60 40 20 0 2π π (A) (B) 0 32 64 96 128 Pixel # ~ 5 ns after SMF 13.9 ps after DCF 470 fs after quadratic/cubic phase equalization Z. Jiang, Leaird, and Weiner, Opt. Lett. 30, 1449 (2005) Phase can be applied modulo 2π. Quadratic, cubic, and higher order phase can be applied independently. Magnitude of phase sweep eventually limited by need to adequately sample using fixed number of pixels

Pulse Shaping in WDM: Dispersion Compensation Research AWG pulse shaper and phase mask Grating pulse shaper and MEMS deformable mirror array Takenouchi, Goh and Ishii, OFC 2001 (NTT) ( ) τ ω = ψ ( ω) ω AWG pulse shaper and deformable mirror Sano et al, OFC 2003 (Sumitomo) VIPA pulse shaper and curved mirror Neilson et al, JLT 22, 101 (2004) [Lucent] Shirasaki and Cao, OFC 2001 (Fujitsu/Avanex) Either colorless dispersion compensation or independent fine-tuning of different channels

Post-compensation of Pulse Distortion in a 100-fs Chirped-Pulse Amplifier SHG-FROG trace of original, phase distorted amplified pulses SHG-FROG trace after phase equalization Phase equalization compresses the pulse close to the bandwidth-limit! Brixner, Strehle, and Gerber, Appl. Phys. B 68, 281 (1999)

High Power Pulse Compression in the 5-fs Regime MIIPS traces pre compensation post compensation Phase scan (rad) Compression results Pulse shaper used both for measurement* and compensation! *Multiphoton intrapulse interference phase scan (MIIPS) -e.g., Xu, Gunn, Dela cruz, Lozovoy and Dantus, JOSA B 23, 750 (2006) Wang, Wu, Li, Mashiko, Gilbertson, and Chang, Optics Express 16, 14448 (2008)

Ultrabroadband Radio-Frequency Photonics RF Arbitrary Waveform Generation 1.2/2.5/4.9 GHz FM Waveform 48/24 GHz FM Waveform THz Phase Modulation RF Optical -2-1 0 1 2 3 Time (ns) -2 0 2 Time (ps) Exploitation of optical pulse shaping technology for cycle-by-cycle synthesis of arbitrary RF waveforms beyond the speed of electronics solutions Approach scales from Gigahertz to Terahertz

Impulse Excitation of Frequency-Independent Antennas Precompensation of antenna dispersion Input voltage Impulse ~195 ps Output voltage Chirped: ~2.17 ns Predistorted Compressed ~264 ps McKinney, Peroulis, and Weiner, IEEE. Trans. MTT (2008)

Polarization Pulse Shaping

Polarization Pulse Shaping 2.40 polariz. component 1 polariz. component 2 Polarization 1 intensity ω (fs -1 ) 2.35 2.30 0 1000 0 1000 3D field representation Polarization 2 intensity Time (fs) 7.5 ps Polarization shaping achieved using +45 o /-45 o dual LCM - without output polarizer Independent phase shaping of two orthogonal polarization components Spectrally, polarization confined to great circle on Poincare sphere Brixner and Gerber, Opt. Lett. 26, 557 (2001)

Polarization Pulse Shaping Near-common-path interferometer approach LCOS SLM example Orthogonal polarizations mapped to different regions of SLM Independent phase and amplitude shaping of two orthogonal polarization components Careful balancing of delays in separate paths (may be aided via pulse shaper) Realization of general frequency-dependent polarization states Masihzadeh, Schlup and Bartels, Optics Express 15, 18025 (2007); Ninck, Galler, Feurer, and Brixner, Opt. Lett. 32, 3379 (2007) ULTRAFAST OPTICS AND OPTICAL FIBER COMMUNICATIONS LABORATORY

Sub-wavelength Control of Nano-optical Fields Tailoring optical near-field on silver nanostructures via adaptive polarization shaping Two photon photoemission electron microscopy images Polarization shaped excitation Polarization-shaped pump plus time-delayed circularly-polarized probe SEM UV Pump only Probe only Pump-probe crosscorrelations Aeschlimann et al, Nature 446, 301 (2007) Aeschlimann et al, PNAS 107, 5329 (2010)

All-order Polarization Mode Dispersion (PMD) Compensation Vector pulse shaping for compensation of vector distortions in fibers τ Differential group delay (DGD) ~800 fs pulse after distortion via ~ 5.5 ps PMD Restored pulse after PMD compensation using custom 4-layer LCM See paper CWI4 Miao, Weiner, Mirkin, and Miller, Opt. Lett. 32, 2360 (2007)

Pulse Shaping at High Spectral Resolution (Towards Longer Time Apertures)

Pulse Shaping at High Spectral Resolution Towards longer time apertures, increased time-bandwidth product Applications in lightwave communications - see e.g. paper CWI4 Resolving individual lines of a frequency comb -fast time structure with long term coherence -line-by-line shaping; optical arbitrary waveform generation

Spectral Line-by-Line Pulse Shaping Shaping: group of lines f rep Frequency domain Shaping: individual lines f rep Μ f rep frequency frequency 1/(Μ f rep ) Repetition period (1/f rep ) Time domain Overlapped regime 1/f rep 1/f rep time 1/f rep 1/f rep Conventional pulse shaping: isolated, low duty factor waveforms Line-by-line spectral filtering: overlapped, 100% duty factor waveforms Sensitive to frequency shifts, pulse-to-pulse phase Additional challenge: line-by-line shaping with period-by-period update? Z. Jiang et al, Opt. Lett. 30, 1557 (2005) time

Harmonic Waveform Generation Line-by-Line Intensity Control, High-Resolution Grating Shaper (~2.5 GHz) Spectra Waveforms 10 GHz 31.5 db (10 db/div) 20 GHz 29 db 400 GHz 28 db Sampling Scope Intensity cross-correlation 500 GHz 26 db 1540 1541 1542 1543 1544 1545 Wavelength (nm) -100-50 0 50 100 Time (ps) Jiang, Leaird, and Weiner, Opt. Exp. 13, 10431 (2005)

Pulse Compression via Line-by-Line Pulse Shaping CW Laser to 5 GHz Subpicosecond Pulse Train Adiabatic soliton compression P h a s e a p p l ie d b y s h a p e r # 1 ( r a d ) 2π π 0 1540 Applied phase 1541 1542 1543 1544 Wavelength (nm) After phase compensation -100 2.4 ps 200 ps Time (ps) After soliton compression 270 fs 200 ps 0 100-100 0 100 Time (ps) Z. Jiang, Huang, Leaird, and Weiner, Nature Photonics 1, 463 (2007)

Complex Shaping at the 100 Line Level a b c Unwrapped phase (rad) d Intensity (a.u.) Intensity (a.u.) 1 0 1 0-200 -100 0 100 200 Time (ps) 0.3 0.3 0.2 0.1 0 15π 2π Measurement Calculation Measurement Calculation -100 Time (ps) -50 15π 0.2 0.1 0 50 Time (ps) Linear plus cubic phase examples Measurement and calculation agree closely: high fidelity waveforms! Spectral phase function Wrapped phase (rad) π 0 1535 1536 1537 1538 1539 1540 Wavelength (nm) Z. Jiang, Huang, Leaird, and Weiner, Nature Photonics 1, 463 (2007)

Virtual Source Array Hyperfine Resolution Spectral Disperser Virtually Imaged Phased Array (VIPA) M. Shirasaki, Opt. Lett. 21, 366 (1996) R r 8 channel demux example: 700 MHz resolution @3 GHz wavelength, 50 GHz free spectral range Fiber Collimator Cylindrical Lens VIPA λ 1 λ2 λ 3 Xiao and Weiner, IEEE PTL 17, 372 (2005) - Offers high spectral resolution, as in a Fabry-Perot - Side-entrance geometry yields angular dispersion via multiple beam interference

Two-Dimensional Grating-VIPA Pulse Shaper with mask This work: Mask with amplitude control In progress: 2D LCOS SLMs (~2,000,000 pixels) Potential for very high waveform complexity without mask * * Virtually imaged phased array -Shirasaki, Opt. Lett. (1996) -Xiao and Weiner, Opt. Express (2004) (or 10 GHz comb) Towards high spectral resolution and broad bandwidth (Long time aperture and narrow pulse features) Supradeepa, Huang, Leaird, and Weiner, Optics Express 16, 11878 (2008) ULTRAFAST OPTICS AND OPTICAL FIBER COMMUNICATIONS LABORATORY

Two Dimensional Disperser Images Wavelength-parallel polarimeter application 1500 channels from 1520-1552.8 nm 50 GHz Wang, Xiao, and Weiner, Opt. Express 13 (2005) 1 GHz Ti:S comb, cavity filtered to 3 GHz Application to comb spectroscopy of iodine Diddams, Hollberg, Mbele (NIST), Nature (2007) pixels (y) 50 100 150 923 MHz Ti:S comb individual lines directly separated Collaboration with JILA Willits, Cundiff, and Weiner, IEEE LEOS Annual Meeting (2008) Supradeepa, et al, Opt. Express 16, 11878 (2008) 200 250 50 100 150 200 250 pixels (x) ULTRAFAST OPTICS AND OPTICAL FIBER COMMUNICATIONS LABORATORY

LARGE Time-Bandwidth Product Pulse Shaping 5GHz features over 8THz bandwidth, more than 1600 features. 150fs input pulse shaped over a 200ps time window. Supradeepa, Huang, Leaird, and Weiner, Optics Express 16, 11878 (2008) ULTRAFAST OPTICS AND OPTICAL FIBER COMMUNICATIONS LABORATORY

Enhanced Spectral Control Demonstration Spatial mask OSA spectra Smallest feature is 10GHz, total bandwidth per spectrum ~4.5THz OSA spectra unraveled ULTRAFAST OPTICS AND OPTICAL FIBER COMMUNICATIONS LABORATORY

Femtosecond Pulse Shaping Generation of user defined ultrafast optical waveforms Control of phase, amplitude, and polarization Broad applications from quantum control to lightwave communications